MEMPHIS, Tenn. — Florida saw its last three seasons end in the Elite Eight. And after handing UCLA a 79-68 Sweet 16 beating Thursday night, the senior-laden Gators are determined not to make it four.

Florida is the NCAA Tournament’s overall top seed and favored to win the Big Dance. After extending their school-record winning streak to 29 games and rolling into Saturday’s South Regional final against No. 11 seed Dayton, apparently nothing less than the whole thing will do.

“We just talked about it and it’s not enough for us,’’ said forward Will Yeguete.

Yeguete is one of four seniors in the Gators’ starting lineup. Florida (35-2) is an anomaly in this era of one-and-dones, and that’s not a bad thing. They grabbed 40 rebounds, held UCLA to 3-of-18 from deep and played with veteran poise and single-mindedness.

“It was possibly my last game of my last season,” senior center Patric Young said. “I’ve never been to the Final Four. We’ve got a chance to be the best team in Florida history. We’ve got an opportunity to win a national championship. What more motivation do you need to go out and play your best?’’

Twelve teams remain after Thursday night’s games.

Who would bet against this team reaching — or even winning — in Dallas? Not the badly beaten Bruins (28-9). Not after Michael Frazier II scored a game-high 19 points and senior guard Scottie Wilbekin — the SEC Player of the Year — added 13, including seven in the game-sealing 10-0, second-half run.

“I like it. Those are the times of the game where the game’s on the line. It’s the [most fun] to play in those type of games,’’ Wilbekin said. “We try to work the ball around, and if it gets to a late clock situation, we try to hit some pick‑and‑roll action or some way where I can try to get in the lane or create for myself or somebody else. So it’s fun. It’s definitely fun being in games like this.’’

They were clinging to a 56-55 lead after UCLA guard Norman Powell made a layup with 10:04 to play, to cap a Bruins run that had erased an 11-point cushion. But the Gators responded with championship mettle, reeling off 10 straight points.

Wilbekin drilled a 3-pointer from the right wing, leaving his shooting hand up for emphasis and sending UCLA scurrying into a timeout with 6:11 to play. It didn’t help. Out of the break, Wilbekin scored again, getting by UCLA forward Travis Wear and drawing a foul for a three-point play and 66-55 lead with 5:34 remaining.

Jordan Adams had a team-high 17 points for UCLA, with sophomore point guard Kyle Anderson — a St. Anthony (N.J.) grad and potential lottery pick — adding 11 points, nine boards and five assists. But it wasn’t enough for UCLA, which lost to Florida in the 2006 national championship, at the 2007 Final Four, in the second round in 2011 and now Thursday.

“We just didn’t have a good game shooting from the perimeter, 3-for-18. It happens like that. It just happened at the wrong time,’’ said Anderson.

Anderson was impressed by the Gators, particularly his counterpart, Wilbeken.

“He was huge. He hit I can remember two big shots down the stretch,” Anderson said. “That’s what you expect out of your senior point guard. He’s been here for four years, Sweet 16 all four years; credit to him.’’